Classwork
All About Alice
Having Your Cake and
Drinking Too
You have found that the additive law of exponents gives an easy way to calculate what
happens to Alice when she eats several pieces of cake. For example, the equation below
shows how to combine the effect of a 17-ounce piece of base 2 cake with that of
a 5-ounce piece of that cake.
217 • 25 = 217 + 5 = 222
You also found out how to combine several servings of the beverage. For example,
here is an equation that shows how to combine the effect of a 4-ounce serving of
base 2 beverage with that of a 9-ounce serving of that beverage.
2 2 = 2 1
4
•
1
9
1
4+9
1
= 2
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Interactive Mathematics Program
All About Alice
Classwork
In this activity, your goal is to figure out how to determine the effect on Alice of
combining base 2 cake and base 2 beverage.
1. What is Alice’s height multiplied by if she consumes the same number of
ounces of cake and beverage? Write an equation using exponential
expressions that expresses your answer.
2. Write at least five ways to combine eating cake with drinking beverage
that will result in Alice being 8 times her original height.That is, find
combinations of amounts of cake and of beverage for which her original
height will be multiplied by 2 3.
3. a.
Find several combinations of amounts of cake and beverage that will result
in Alice being 32 times her original height.
b. Find several combinations of amounts of cake and beverage that will result
in Alice being 4 times her original height.
4. Look for a pattern in your answers to Questions 2 and 3.Write a general
expression for the amount Alice’s height is multiplied by if she eats C ounces
of cake and drinks B ounces of beverage.
5. What happens to your rule in Question 4 if B is more than C?
Interactive Mathematics Program
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